which we call Heat. 121 
it would be reflected, and then commence a similar series of 
journeys to and fro, and so forth. 
Lastly, there is no doubt that actually the greatest possible 
variety exists amongst the velocities of the several molecules. In 
our considerations, however, we may ascribe a certain mean velo- 
city to all molecules. It will be evident from the following for- 
mul, that, in order to maintain an equal pressure, this mean 
velocity must be so chosen that with it the total vis viva of all 
the molecules may be the same as that corresponding to their 
actual velocities. 
16. According to these assumptions, it is evident, that, during 
the unit of time, each molecule will strike the side under consi- 
deration just as often as during that time it can, by following its 
peculiar direction, travel from the side m question to the other 
and back again. Let / be the distance between the large parallel 
sides, and 3 the acute angle between the normal and the direc- 
tion of motion; then ae 5 is the length of the path from one 
side to the other, and 
u.coss 
the number of impulses given to the side, w being the velocity of 
the molecule. 
With respect to the directions of the several molecules, we 
must assume that on the average each direction is equally repre- 
sented. From this it follows, that the number of molecules 
moving in directions which form with the normal angles included 
between 3 and $+ dS, has to the whole number of molecules the 
same ratio that the surface of the spherical zone, whose limiting 
circles correspond to the angles $ and dS, has to the surface of 
the hemisphere, that is, the ratio 
2a sin SdS : 27. 
Hence if n represents the whole number of molecules, the num- 
ber which corresponds to the angular interval between 3 and 
$+4dS will be 
nsin 3d3, 
and the number of shocks imparted by them will be 
nu 
9f Co8 9 sin Sd3. RS er) Ae 
17. In order to determine the intensity of a shock, the whole 
velocity must be resolved into two components, one parallel and 
the other perpendicular to the side. Of these components, the 
first will not be affected by the shock, and will not enter into 
